Many existing migration schemes cannot simultaneously handle the two most important problems of migration: imaging of steep dips and imaging in media with arbitrary velocity variations in all directions. For example, phase‐shift (ω, k) migration is accurate for nearly all dips but it is limited to very simple velocity functions. On the other hand, finite‐difference schemes based on one‐way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events. We propose a new hybrid migration method, named “Fourier finite‐difference migration,” wherein the downward‐continuation operator is split into two downward‐continuation operators: one operator is a phase‐shift operator for a chosen constant background velocity, and the other operator is an optimized finite‐difference operator for the varying component of the velocity function. If there is no variation of velocity, then only a phase‐shift operator will be applied automatically. On the other hand, if there is a strong variation of velocity, then the phase‐shift component is suppressed and the optimized finite‐difference operator will be fully applied. The cascaded application of phase‐shift and finite‐difference operators shows a better maximum dip‐angle behavior than the split‐step Fourier migration operator. Depending on the macro velocity model, the Fourier finite‐difference migration even shows an improved performance compared to conventional finite‐difference migration with one downward‐continuation step. Finite‐difference migration with two downward‐continuation steps is required to reach the same migration performance, but this is achieved with about 20 percent higher computation costs. The new cascaded operator of the Fourier finite‐difference migration can be applied to arbitrary velocity functions and allows an accurate migration of steeply dipping reflectors in a complex macro velocity model. The dip limitation of the cascaded operator depends on the variation of the velocity field and, hence, is velocity‐adaptive.

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Geological Aims, Planning, Field Investigations Purpose of the InvestigationsThe seismic lines discussed in this paper explore a central part of the Variscan Belt of Europe. This belt is more than 1000 km wide and can be subdivided -in the Central European segment -into several zones, which were first recognized by Kossmat (1927). The zonal boundaries are now regarded as sutures which originated from the closure of several Paleozoic basins. First results on the geophysical-gelogical investigations in the Oberpfalz area are found in DEKORP Research Group (1988).The DEKORP 4 and 4-Q lines, as well as the closely related KTB 8501 to 8506 lines, were intended to scan the border zone between the Moldanubian Zone and the northward adjacent Saxothuringian Zone (Fig. 1). The Saxothuringian (ST) represents the infill of a basin which opened during the Cambro-Ordovician beyond the rift stage at least into a narrow ocean, and the Moldanubian (MN) contains blocks of pre-Variscan crust (and their Paleozoic cover) which were reactivated by the Variscan orogeny and thrusted toward the NW over the Saxothuringian foreland. Tectonic deformation and co-related metamorphism are polyphase and have produced a highly complex crustal structure For more detailed information see Franke (this Vol.). Special emphasis has been put on the area S of Erbendorf which was under consideration and has since been selected as the site of the Continental Deep Drilling Project KTB.The long DEKORP 4 profile was intended as a general cross-section from the Teuschnitz syncline in the N to the MN rocks in the S. The KTB 8501 to 8506 lines were arranged in form of a grid to explore the ST/MN boundary region near Erbendorf (i.e., around the KTB drilling site). This array of lines (Fig. 1) represents a first step in obtaining a 3-D view of the target area.The DEKORP 4-Q line is positioned at a right angle with respect to the DEKORP 4 line near its southern end. It was intended to investigate important tectonic structures such as the Bavarian "Pfahl" and the R.

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